Lie product and fixed points preservers
Abstract
Let B(X) be the algebra of all bounded linear operators on a complex Banach space X . In this paper, it is determined the form of surjective maps φ : B(X ) → B(X ) that satisfy F (φ (A)φ (B) − φ (B)φ (A)) = F (AB − BA) for every A,B ∈ B(X), where F(A) denotes the set of all fixed points of an operator A ∈ B(X).
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